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Ordered Permutation Groups : Economic and Social Studies / National Institute of Economic - A. M. W. Glass

Ordered Permutation Groups

Economic and Social Studies / National Institute of Economic

Paperback

Published: 8th March 1982
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As a result of the work of the nineteenth-century mathematician Arthur Cayley, algebraists and geometers have extensively studied permutation of sets. In the special case that the underlying set is linearly ordered, there is a natural subgroup to study, namely the set of permutations that preserves that order. In some senses. these are universal for automorphisms of models of theories. The purpose of this book is to make a thorough, comprehensive examination of these groups of permutations. After providing the initial background Professor Glass develops the general structure theory, emphasizing throughout the geometric and intuitive aspects of the subject. He includes many applications to infinite simple groups, ordered permutation groups and lattice-ordered groups. The streamlined approach will enable the beginning graduate student to reach the frontiers of the subject smoothly and quickly. Indeed much of the material included has never been available in book form before, so this account should also be useful as a reference work for professionals.

Opening the innings
Introduction
Doubly Transitive A
The structure theory
Congruences and blocks
Primitive ordered permutation groups
The wreath product
Applications to ordered permutation groups
Simple-permutation groups
Uniqueness of representation
Pointwise suprema and closed subgroups
Applications to lattice-ordered groups
Embedding theorums for lattice-ordered groups
Normal valued lattice-ordered groups
The author's perogative
Algebraically closed lattice-ordered groups
The word problem for lattice-ordered groups
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521241908
ISBN-10: 0521241901
Series: Economic and Social Studies / National Institute of Economic
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 332
Published: 8th March 1982
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.88
Weight (kg): 0.49